EPIMK2-an innovative stiff systems solver. We demonstrate that a simple modification of existing algorithms for the solution of stiff differential equations may be developed through a transformation of the original differential equation, to develop a less- stiff form of the original differential equation(s). We are concerned with numerical solutions of the initial value problem (1)y ’ =f(t,y),y(0)=y 0 , where y, f, and y 0 are vectors of length n. By stiffness, we mean the property that some eigenvalues of the Jacobian matrix, J=∂f/∂y have large magnitude relative to an appropriate time-scale for the problem. If τ represents an appropriate time-scale for observation of a physical phenomenon described by the problem, then the problem would be considered stiff if τ|λ i (J)|≫1· EPISODE is a large and complex set of FORTRAN programs which produce, at time T, a solution to the initial-value problem (1) according to error criteria encoded and supplied by the user. EPISODE consists of a number of different algorithms for different problem classes.

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  1. Lawson, J.D.; Swayne, D.A.: EPIMK2-an innovative stiff systems solver (1986)